hey /sci/, im new here:

i've heard from various places on the internet a claim along the lines of "category theory seeks to construct a new foundation of mathematics".

now this doesn't make any sense to me because iirc 1. set theory (and its various formulations) are 1.1 pretty much all that we have (at least used in practice) 1.2 itself studied in category theory/ im guessing that the interpretation of the word "foundation" should be different from the interpretation of "set theory is the /foundation/ of modern math", but without a gauge of what category theory is about, i don't really know how to engage with this.

normally i should be studying the subject itself, but allegedly the content has a very high barrier of entry (a lot of prerequisites?) before the stuff starts to make sense, so i was wondering what /sci/ has to say about it.

also desu, is it just a ~meme~? i find it hard to verbalize what i mean, but field feels pretty iffy for some reason, but i can accept the possibility that its a problem on my part. though it doesn't seem like category theory does much outside of its domain

alternatively: what is category trying to achieve?